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963, 3848, 8655, 15384, 24035, 34608, 47103, 61520, 77859, 96120, 116303, 138408, 162435, 188384, 216255, 246048, 277763, 311400, 346959, 384440, 423843, 465168, 508415, 553584, 600675, 649688, 700623, 753480, 808259, 864960, 923583, 984128
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OFFSET
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1,1
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COMMENTS
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The identity (961*n+1)^2-(961*n^2+2*n)*(31)^2=1 can be written as A158414(n)^2-a(n)*(31)^2=1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(31^2*t+2)).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(963+959*x)/(1-x)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {963, 3848, 8655}, 50]
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PROG
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(MAGMA) I:=[963, 3848, 8655]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 961*n^2 + 2n.
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CROSSREFS
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Cf. A158414.
Sequence in context: A031740 A031529 A031709 * A252413 A267973 A267996
Adjacent sequences: A158410 A158411 A158412 * A158414 A158415 A158416
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 18 2009
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STATUS
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approved
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